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In this paper we present a comprehensive framework for learning robust low-rank representations by combining and extending recent ideas for learning fast sparse coding regressors with structured non-convex optimization techniques. This…

Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…

We propose a low-rank transformation-learning framework to robustify subspace clustering. Many high-dimensional data, such as face images and motion sequences, lie in a union of low-dimensional subspaces. The subspace clustering problem has…

Contrast enhanced ultrasound is a radiation-free imaging modality which uses encapsulated gas microbubbles for improved visualization of the vascular bed deep within the tissue. It has recently been used to enable imaging with unprecedented…

High-sensitivity clutter filtering is a fundamental step in ultrasound microvascular imaging. Singular value decomposition (SVD) and robust principal component analysis (rPCA) are the main clutter filtering strategies. However, both…

Sparse and outlier-robust Principal Component Analysis (PCA) has been a very active field of research recently. Yet, most existing methods apply PCA to a single dataset whereas multi-source data-i.e. multiple related datasets requiring…

Principal Components Analysis (PCA) is one of the most widely used dimension reduction techniques. Robust PCA (RPCA) refers to the problem of PCA when the data may be corrupted by outliers. Recent work by Cand{\`e}s, Wright, Li, and Ma…

Robustness is a fundamental property of machine learning classifiers required to achieve safety and reliability. In the field of adversarial robustness of image classifiers, robustness is commonly defined as the stability of a model to all…

Object-centric representation learning offers the potential to overcome limitations of image-level representations by explicitly parsing image scenes into their constituent components. While image-level representations typically lack…

In recent work, robust Principal Components Analysis (PCA) has been posed as a problem of recovering a low-rank matrix $\mathbf{L}$ and a sparse matrix $\mathbf{S}$ from their sum, $\mathbf{M}:= \mathbf{L} + \mathbf{S}$ and a provably exact…

This work presents a novel approach for robust PCA with total variation regularization for foreground-background separation and denoising on noisy, moving camera video. Our proposed algorithm registers the raw (possibly corrupted) frames of…

This work presents a new robust PCA method for foreground-background separation on freely moving camera video with possible dense and sparse corruptions. Our proposed method registers the frames of the corrupted video and then encodes the…

Many real-world datasets contain hidden structure that cannot be detected by simple linear correlations between input features. For example, latent factors may influence the data in a coordinated way, even though their effect is invisible…

Deep unfolded neural networks are designed by unrolling the iterations of optimization algorithms. They can be shown to achieve faster convergence and higher accuracy than their optimization counterparts. This paper proposes a new…

Dynamic robust PCA refers to the dynamic (time-varying) extension of robust PCA (RPCA). It assumes that the true (uncorrupted) data lies in a low-dimensional subspace that can change with time, albeit slowly. The goal is to track this…

Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA). Prior studies have demonstrated that linear autoencoders (LAEs) can recover the ordered, axis-aligned principal components of PCA by…

The robust PCA problem, wherein, given an input data matrix that is the superposition of a low-rank matrix and a sparse matrix, we aim to separate out the low-rank and sparse components, is a well-studied problem in machine learning. One…

High-dimensional data sets are often analyzed and explored via the construction of a latent low-dimensional space which enables convenient visualization and efficient predictive modeling or clustering. For complex data structures, linear…

In recent years, multimodal anomaly detection methods have demonstrated remarkable performance improvements over video-only models. However, real-world multimodal data is often corrupted due to unforeseen environmental distortions. In this…

Robust PCA has drawn significant attention in the last decade due to its success in numerous application domains, ranging from bio-informatics, statistics, and machine learning to image and video processing in computer vision. Robust PCA…